Acoustic scattering from inhomogeneous spheres with impenetrable cores

Abstract

In this work, we develop a full wave solution for the acoustic scattering by inhomogeneous compressibility spheres having an impenetrable core. The solution is developed by following two alternative mathematical formulations: one through a volume integral equation where a modified Green's function is needed to describe the scattering by the impenetrable core, and one through a surface-volume integral equation where the equivalent surface sources due to the impenetrable core are described via a surface integral. We prove analytically that these two alternative paths lead to the same set of nonhomogeneous equations for the evaluation of the total acoustic field. We investigate both Dirichlet and Neumann boundary conditions. Our developed method is then numerically validated by comparison with other techniques, including the exact solution for core-mantle spheres with constant compressibility function. Furthermore, we construct a solution which is valid for a special inhomogeneous compressibility profile based on the Nomura-Takaku distribution, which allows to construct the solution based on the separation of variables. Thus, the proposed method is further validated for inhomogeneous functions. New numerical results are presented for the interior and scattered acoustic fields for various inhomogeneous profiles.